Deploy Qt 5.1 app on Linux

As most Linuxes (Linuxii?) only officially distribute 4.8, I would like to figure out how to distribute our app with 5.1, which we do on Windows and Mac. In the past when I have tried this by recompiling Qt, it seemed to lead to a rabbit hole of dependencies. I could get Qt to work, but then it would have trouble finding the image and sound libraries needed. And getting those compiled led to further incompatibilities.

Is there a "definitive" page showing "best practices" for shipping a Qt 5.1 app that depends on WebKit, images, and sound to work?